Toulouse -LRB- CNN -RRB- -- French police had no grounds on which to arrest gunman Mohammed Merah before he carried out three attacks in which seven people died , Prime Minister Francois Fillon told French radio station RTL Friday .

Merah , 23 , who was shot dead by special forces Thursday after a siege lasting more than 30 hours in the southwestern city of Toulouse , was wanted in the killings of three French paratroopers , a rabbi and three children ages 4 , 5 , and 7 .

Merah , a French citizen of Algerian descent , had been put under surveillance after trips to Afghanistan and Pakistan , officials have said , leading commentators to ask why he was not stopped sooner .

He claimed to have attended an al Qaeda training camp , according to Paris prosecutor Francois Molins , and was on the U.S. no-fly list for that reason , a U.S. intelligence official said .

And Toulouse lawyer Eric Mouton , acting for a woman named only as Aicha , to protect her privacy , told CNN she filed a complaint against Merah in 2010 over alarming behavior Merah displayed toward her children .

Aicha claimed that Merah had beaten up her daughter , 19 at the time , and held her son , 15 , against his will in a room for several hours , forcing him to watch videos of violent combat and of people 's throats being slit .

Mouton said he would meet with Toulouse prosecutor Michel Valet later Friday to discuss the case . It is not known if any action was taken against Merah at the time .

Fillon defended the police and intelligence services , saying they had done a remarkable job in finding the killer within 10 days of the first attack , on March 11 .

Fillon acknowledged that some questions should be asked , particularly with regard to surveillance .

But , he said , `` there was no single element '' that would have allowed the police to arrest Merah before the killings began .

`` We do n't have the right in a country like ours to keep under permanent surveillance without a judicial decision someone who has committed no offense , '' he told RTL . `` We live in a country under the rule of law . ''

Crowds gathered in a square in central Toulouse at noon Friday to remember those killed in the attacks .

Toulouse Mayor Pierre Cohen called the rally in solidarity with the families of the victims and as a demonstration of unity against anti-Semitism and racism , CNN affiliate BMF-TV reported .

CNN iReporter Henry Krisch said the mood at the commemoration was `` eerily silent and depressed , '' as the names of the seven dead were read out and a minute 's silence was held .

Meanwhile , investigators carrying shovels , metal detectors and hammers re-entered Merah 's apartment Friday , continuing their search of the premises .

A police cordon surrounding the property was removed in the afternoon , exposing the messy aftermath of the gun siege to those at the scene .

The first floor balcony from which Merah jumped , still firing , before being shot in the head , has been boarded up . Bullet holes pock the walls and nearby cars , and broken glass lies scattered around .

Elizabeth Allannic , a spokeswoman for the Paris prosecutor , said the detention of Mohammed Merah 's mother , brother and his brother 's girlfriend had been extended Friday .

Police tracked Merah down via his mother 's computer IP address , which was apparently used to respond to an ad posted by the first victim , officials said . Interior Minister Claude Gueant initially told reporters it was the IP address of Merah 's brother that led investigators to him .

Fillon said the French domestic intelligence service , the DCRI , had done its job `` perfectly well , it identified Mohammed Merah when he traveled to Afghanistan and Pakistan , it questioned him and it monitored him , he was under surveillance , on a list , and it was thanks to that listing that he was identified .

`` It watched him for the necessary period , and it led to the conclusion that there was no indication or trace that Mohammed Merah was a dangerous man . ''

Investigations will determine whether Merah acted alone , the prime minister told RTL . He added : `` We must not mix religious fundamentalism with terrorism . ''

French President Nicolas Sarkozy vowed increased legal measures to punish those who pursue extremist activities online or travel overseas for indoctrination and training .

He spoke Thursday as campaigning resumed for the French presidential election , with the first round of voting due next month .

Rival candidate Francois Hollande , appearing at a rally Thursday night , said questions will have to be asked about the Merah case , French media reported .

Earlier , French Foreign Minister Alain Juppe told radio network Europe 1 that `` light must be shed '' on events leading up to the shootings by Merah .

`` I understand that one can ask whether there was a failing or not . As I do n't know if there was a failing , I ca n't tell you what kind of failing , but light must be shed on that , '' Juppe said .

The day after his third and final attack , on a Jewish school , Merah was tracked down to an apartment in Toulouse , where a siege began in the early hours Wednesday .

It finally came to a bloody end Thursday morning , when Merah emerged from a bathroom in his apartment and fired more than 30 shots at police who had burst in to end the standoff , Molins said .

Merah then jumped out a window onto a balcony , still shooting , and was found dead on the ground , officials said .

He died from a gunshot wound to the head , Molins said .

After Merah 's death , Sarkozy said everything had been done to bring him to justice alive but security forces could not be exposed to further risk .

Authorities said the young man cited a variety of reasons for the killings , including the missions of French troops abroad , the oppression of Palestinians and France 's ban on the wearing of Islamic veils .

After Merah was killed , police found video he had recorded of the attacks , ammunition and ingredients for explosives , Molins said .

In the video of the first shooting of a French soldier in Toulouse , Merah told the soldier , `` You kill my brothers , I kill you , '' Molins told reporters . Another video shows Merah gunning down two more French soldiers in Montauban . He is heard saying `` Allahu Akbar , '' or `` God is great , '' Molins said .

Gueant said Merah had been under surveillance by French intelligence for years .

He had `` already committed certain infractions , some with violence , '' Gueant said .

Merah was sentenced 15 times by a Toulouse juvenile court when he was a minor , Molins said . The charges mostly involved theft .

In the first shooting on March 11 , Imad Ibn Ziaten , a paratrooper of North African origin , arranged to meet a man in Toulouse who wanted to buy a scooter Ziaten had advertised online , the interior minister said . The victim said in the ad that he was in the military .

Four days later , two other soldiers were shot dead and another injured by a black-clad man wearing a motorcycle helmet in a shopping center in the city of Montauban , about 50 kilometers -LRB- 30 miles -RRB- from Toulouse .

In the attack at the private Jewish school Ozar Hatorah on Monday , a man wearing a motorcycle helmet and driving a motor scooter pulled up and shot a teacher and three children -- two of them the teacher 's young sons -- in the head . The other victim , the daughter of the school 's director , was killed in front of her father .

Police said the same guns were used in all three attacks .

CNN 's Diana Magnay , Saskya Vandoorne , Anna Prichard and Alex Felton contributed to this report .

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NEW : Witness : The mood was silent and somber as the victims ' names were read out at a rally

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Bullet holes pock the walls of the apartment where Merah holed up , and nearby cars

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A mother filed a complaint against Merah in 2010 , saying he threatened her children

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Prime Minister Francois Fillon says police and intelligence services did well